Question

∠1 is a complement of ∠2.
∠2≅∠3
m∠1 + m∠2 = 90°
m∠2 = m∠3
definition of congruent angles
substitution property of equality
∠1 is a complement of ∠3.

Explanation:

Step1: Recall complement definition

Given $\angle1$ is a complement of $\angle2$, so $m\angle1 + m\angle2=90^{\circ}$ by the definition of complementary angles.

Step2: Use congruent - angle property

Since $\angle2\cong\angle3$, then $m\angle2 = m\angle3$ by the definition of congruent angles.

Step3: Apply substitution

Substitute $m\angle2$ with $m\angle3$ in the equation $m\angle1 + m\angle2 = 90^{\circ}$. We get $m\angle1 + m\angle3=90^{\circ}$.

Step4: Determine complement relationship

By the definition of complementary angles, since $m\angle1 + m\angle3 = 90^{\circ}$, $\angle1$ is a complement of $\angle3$.

Answer:

$\angle1$ is a complement of $\angle3$ because $m\angle1 + m\angle3 = 90^{\circ}$ which is derived from the given $\angle1$ is a complement of $\angle2$ ($m\angle1 + m\angle2=90^{\circ}$), $\angle2\cong\angle3$ (so $m\angle2 = m\angle3$) and the substitution property of equality.